We propose a method for the fabrication of the mirror elements that compose the complex-shaped fly-eye mirrors for use in an extreme ultraviolet lithography (EUVL) system. In this method, silicon blocks are polished to have a spherical shape and smoothness, from which the mirror elements are cut out by wire electrical discharge machining. Thus, this method enables more effective fabrication of the mirror elements than the method proposed previously. To evaluate the effectiveness of the present method, the mirror elements having a flat reflective surface are fabricated as a preliminary experiment. The resultant mirror elements have highly accurate and smooth surfaces, although they have a unique shape compared to that of general optics. Moreover, to construct the fly-eye mirror, we propose a method for arranging the mirror elements, in which mirror elements are fixed to a base plate containing magnets. This allows the accurate arrangement of all the reflective surfaces relative to the base plate. To enable their attraction to the magnets, the bottom of the silicon mirror elements is plated with metal. Experiments confirm the mirror elements are accurately arranged. Thus, we demonstrate that the proposed methods are useful in realizing the fly-eye mirror.